Local Monotonicity Reconstruction

We propose a general model of local property reconstruction. Suppose we have a function f on domain Γ, which is supposed to have a particular property P, but may not have the property. We would like a procedure which produces a function g that has property P and is close to f (according to some suitable metric). The reconstruction procedure, called a filter, has the following form. The procedure takes as input an element x of Γ and outputs g(x). The procedure has oracle access to the function f and uses a single short random string ρ, but is otherwise deterministic. This model was inspired by a related model of online property reconstruction that was introduced by by Ailon, Chazelle, Comandur and Liu (2004). It is related to the property testing model, and extends the framework that is used in the model of locally decodable codes. A similar model, in the context of hypergraph properties, was independently proposed and studied by Austin and Tao (2008). We specifically consider the...

• Type: Journal
• Year: 2010
• Where: SIAMCOMP
• Authors: Michael E. Saks, C. Seshadhri
• Keywords: Model, Procedure, Property Reconstruction, SIAMCOMP 2010